Quantum partial coherence measures constructed from Fisher information

Abstract

Quantum mechanics gives a new breakthrough to the field of parameter estimation. In the realm of quantum metrology, the precision of parameter estimation is limited by the quantum Fisher information. We introduce the measures of partial coherence based on (quantum) Fisher information by taking into account the post-selective non-unitary parametrization process. These partial coherence measures present a clear operational interpretation by directly linking the coherence to the parameter estimation accuracy. Furthermore, we explore the distinctions between our partial coherence measure and the quantum Fisher information within the context of unitary parametrization. We provide an analytical expression for the partial coherence measure of two-qubit states. We elucidate the operational significance of the partial coherence measures by establishing the connections between the partial coherence measures and quantum state discrimination.